They can, but in doing so they open themselves to some liability. The exact extent varies based on your jurisdiction and you should consult your attorney for details. The basic guidelines in the US are:
- If the medications are in a first-aid kit in a general workspace that people can access on their own, the employer can post a sign about how taking the medications is at employees own risk. As long as the employer ensures that the medications are not expired/damaged, this absolves them of most liability
- If OTC meds are distributed to an employee from another employee/owner directly, liability exists.
